Try this, a good detailed descriptions of HP solvers.

http://www.finseth.com/hpdata/solvers.html

To my mind, the best solver is the one featured on 17BII/19BII; also in 27S, even though it does not seem to have symbolic simplification (which is transparent in the user interface).

More than a solver, this is a true programming language, almost as powerful as BASIC (unfortunately, the lack of user-defined functions limits its power). The L() and G() functions allows intermediate variables and true programming. A pity that despite this, the 17BII/19BII/27S are often refered to as 'non-programmable devices' !!

Next would be the 42S solver, which lacks algebraic equation entry (RPN is nice, but NOT for equation entry) and forces you to 'MVAR' any variable supposed to appear in the menu (But let you access to the full power of RPN programming). A pity, really - think of the killer machine a merge of 42S and 27S would be...

Next, the 32SII/33S solver - neat, simple to use, well integrated with RPN (a unique case in HP calcs of harmony between RPN and algebraic equations), but with severe limitations: no editing capabilities of equations, no long variable names, no implicit multiplication (a nonsense when you don't have long variable names - you could have at least the benefit when you pay for the cost !), and somewhat clumsy interface (you need to circulate through all variables instead of the neat menus of 17BII/19BII/27S/42S). However, this works well for most problems.

Hope this helps.

Cheers,

Vincent